Stoichiometry: 3.403 - Gas volumes

Gases, involved in chemical reactions show simple ratios between gas volumes. This makes dealing with gaseous reactions very simple in terms of calculations.

Syllabus reference

Structure 1.4.6 - Avogadro’s law states that equal volumes of all gases measured under the same conditions of temperature and pressure contain equal numbers of molecules.

Solve problems involving the mole ratio of reactants and/or products and the volume of gases.

Guidance

Tools and links

Structure 1.5 - Avogadro’s law applies to ideal gases.
Under what conditions might the behaviour of a real gas deviate most from an ideal gas?

Gay Lussac's law
Avogadro's hypothesis

Gay Lussac's law

In 1808 the Freanch chemist Gay Lussac investigating the reactions of gases came to the conclusion that when gases combine chemically they do so in volumes that have a simple ratio to one another, and to any gaseous product, provided that all gases are measured at the same temperature and pressure. This became known as Gay Lussac's law.

For example, in the reaction between hydrogen and oxygen making water:

hydrogen + oxygen

water
2H₂ + O₂

2H₂O

The volume of hydrogen needed for complete reaction is always double the volume of oxygen, provided the temperature and pressure of the two gases are the same.


2 volumes of hydrogen		1 volume of oxygen

Avogadro's hypothesis

Extending Gay Lussac's work in 1811, Avogadro suggested that "equal volumes of all gases contain equal number of molecules (the gases being measured at the same temperature and pressure). This became known as Avogadro's hypothesis or Avogadro's law.

This means that in the reaction:

N₂ + 3H₂ 2NH₃

For a given volume of nitrogen, three times the volume of hydrogen is needed for complete reaction. The volume of nitrogen contains a certain number of molecules and there are three times as many molecules in the volume of hydrogen.

N₂	+	3H₂	2NH₃
1 molecule	+	3 molecules	2 molecules
1 volume	+	3 volumes	2 volumes

Avogadro's hypothesis allows us to substitute the coefficients of any balanced gaseous equation for volumes of gas, for example:

Example: Find the volume of hydrogen required to react completely with 200 cm³ of nitrogen according to the equation:

N₂ + 3H₂ 2NH₃

The equation tells us that 1 volume of nitrogen reactrs completely with 3 volumes of hydrogen:

Therefore volume of hydrogen = 3 x volume of nitrogen

Therefore volume of hydrogen = 3 x 200 cm³ = 600 cm³

Example:

Using the equation:

N₂ + 3H₂ 2NH₃

if 100 cm³ of nitrogen was used (this is now equivalent to 1 'volume') it would need 3 times as much hydrogen for complete reaction i.e. 3 volumes = 300 cm³.

The reaction would produce 2 volumes of ammonia i.e. 2 x 100 cm³ = 200 cm³

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